In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are 3 marks for each correct answer, - 2 marks for each wrong answer and 0 mark if the question is not

Question

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Correct answer: 0

Let the marks obtained in each of the five MCQ be ${x}_{1}, {x}_{2}, {x}_{3}, {x}_{4}, {x}_{5}$

Now, ${x}_{1} + {x}_{2} + {x}_{3} + {x}_{4} + {x}_{5} = 5$

Only one possibility satisfies the above equation i.e. $3, 3, 3, - 2, - 2$

Hence, total number of ways $= \dfrac{5 !}{3 ! 2 !} \times 2 \times 2 = 40$

In an examination, there are 5 multiple choice questions with 3...

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